On two forms of Fisher's measure of information (Journal article)

Papaioannou, T./ Ferentinos, K.

Fisher's information number is the second moment of the "score function" where the derivative is with respect to x rather than theta. It is Fisher's information for a location parameter, and also called shift-invariant Fisher information. In recent years, Fisher's information number has been frequently used in several places regardless of parameters of the distribution or of their nature. Is this number a nominal, standard, and typical measure of information? The Fisher information number is examined in light of the properties of classical statistical information theory. It has some properties analogous to those of Fisher's measure, but, in general, it does not have good properties if used as a measure of information when theta is not a location parameter. Even in the case of location parameter, the regularity conditions must be satisfied. It does not possess the two fundamental properties of the mother information, namely the monotonicity and invariance under sufficient transformations. Thus the Fisher information number should not be used as a measure of information (except when theta a location parameter). On the other hand, Fisher's information number, as a characteristic of a distribution f(x), has other interesting properties. As a byproduct of its superadditivity property a new coefficient of association is introduced.
Institution and School/Department of submitter: Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών
Keywords: additivity,convolutions,cramer-rao inequality,fisher information,fisher information number,limit theory,maximal information,observed and expected fisher information,shift-invariant fisher information,superadditivity,inequality,dependence,matrix,superadditivity
URI: http://olympias.lib.uoi.gr/jspui/handle/123456789/13286
ISSN: 0361-0926
Link: <Go to ISI>://000231005000003
Appears in Collections:Άρθρα σε επιστημονικά περιοδικά ( Ανοικτά)

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